The Supreme Court heard a challenge to President Obama's policies on immigration Monday morning, a politically sensitive case that could affect millions of people living in the United States illegally and their families.

The Obama administration has sought to offer some undocumented immigrants a guarantee that they would be allowed to stay in the United States temporarily. The president's done so in two steps. In 2012, he allowed undocumented immigrants brought to the United States at a young age to apply for a temporary reprieve from deportation. Then, in 2014, he expanded on the policy by including older undocumented immigrants who had come as children in the policy, as well as the undocumented parents of U.S. citizens.

Republicans view the policy overall as a kind of amnesty that the president does not have the authority to grant, and so far, they've successfully stymied the 2014 expansion in the courts. The Supreme Court will rule, likely in June, about whether that second proposal can proceed.

To qualify for a reprieve from deportation under Obama's 2014 proposal, an immigrant would have had to satisfy a number of requirements. Here's a closer look at the immigrants whose futures the justices considered Monday.

How many people could be affected by the Supreme Court's decision?

The plan Obama put forward in 2014 would offer relief to two broad categories of undocumented immigrants.

The first includes parents whose children who are citizens or legal permanent residents. This group includes about 3.6 million people, according to estimates from the Migration Policy Institute. Many of them came to the United States illegally but are the parents of citizens because their children were born here. Together with their families, according to the institute, there are at least 10 million people (including legal immigrants, citizens and undocumented immigrants) who live in households that would be affected by this rule.

The second group includes the immigrants who were brought here illegally as children and were not granted a reprieve under the 2012 action. The 2014 proposal would have expanded that group by 300,000 to include older immigrants and more recent arrivals. The statuses of the 1.2 million who already applied under the policy from 2012 are not at issue in the Supreme Court's case Monday.

The following chart shows the total number of people who would be affected by the court's ruling -- 4 million.

Who would be affected?

If the court rules against the Obama administration, all 4 million of those undocumented immigrants would lose the opportunity to participate in the policies. But if it rules in favor, immigrants would still have to satisfy a number of requirements to qualify.

For the parents of citizens or legal permanent residents, their children would have to have been born before Nov. 21, 2014 -- the date of Obama's recent executive action -- and the parents would have to have been in this country the day before. They also would have to have lived in the United States since at least Jan. 1, 2010, and they'd have to pay taxes to win the reprieve.

For children brought here illegally, they must have arrived before Jan. 1, 2010 and before their 16th birthdays. They also would have to be in school, have graduated or earned a GED or have been honorably discharged from the military.

The diagram below illustrates which immigrants would be eligible for a reprieve from deportation if the Obama administration wins its case in the Supreme Court. If the administration loses the argument, most immigrants who arrived as children would still be eligible under the 2012 policy.

What will the court's decision mean in practice?

If the next president is a Republican, he might end Obama's program even if the court allows it to proceed for now, rendering the decision moot. If, by contrast, a Democrat wins in November, and the court upholds Obama's plan, many undocumented immigrants will benefit from the program.

Obama would not only grant them permission to stay in the country temporarily. They could also apply to work while they are here, meaning they'd be able to earn more money for their families. They wouldn't be limited only to employers who overlook fraudulent or nonexistent immigration paperwork, and they could find jobs that better suit their skills.

According to a recent report that the Migration Policy Institute published together with the Urban Institute, a typical family with parents eligible under the president's plan because the children are citizens or permanent residents would earn about $3,000 more per year on average. Their incomes would increase by 10 percent, in other words.

The authors of the report accounted for differences in immigrants' age, education and proficiency in English, among other factors. Examining the families in this group that are currently living in poverty, the researchers concluded that one in six would no longer be poor if they were allowed to work.